Net present value (NPV)
The present value of all future cash flows minus the upfront cost; positive means the investment beats your discount rate.
NPV = −C0 + Σ CFt ÷ (1 + r)^t
Explanation
NPV starts with a discounted cash flow valuation and subtracts what you pay today. The result is the value the investment adds, in today’s dollars, compared with earning your discount rate instead.
- NPV above zero: the investment earns more than the discount rate.
- NPV of zero: it earns exactly the discount rate.
- NPV below zero: it earns less than the discount rate.
NPV is useful for comparing choices of different sizes and timing, such as paying down a mortgage versus investing, buying versus renting, or whether an extra year of work is worth it. Because it depends on the discount rate, the answer can flip if you change the rate. That is not a flaw; it reflects the fact that a decision can be good at one hurdle rate and bad at another.
In scenarios, comparing two plans side by side in today’s dollars is an NPV-style comparison: the app discounts the differences between them back to the present.
Example
You pay $10,000 today for something that returns $4,000 at the end of each of the next three years. Your discount rate is 8%.
- Year 1: $4,000 ÷ 1.08 = $3,703.70
- Year 2: $4,000 ÷ 1.1664 = $3,429.36
- Year 3: $4,000 ÷ 1.2597 = $3,175.33
- Present value of inflows: $10,308.39
- NPV = $10,308.39 − $10,000 = +$308.39
At 8%, it is worth doing. At a 12% discount rate the inflows are worth only $9,607.33, so NPV = −$392.67, and it is not. The break-even rate, where NPV is exactly zero, is the internal rate of return (about 9.7% here).